Subfields of the function field of the deligne-Lusztig curve of ree type

Çakçak, Emrah
Let X be the Deligne-Luzstig curve of Ree type defined over ¥q,q = 32s+1, s > 1 and F its function field. One of the main problem here is to construct a large number of nonrational subfields of F and compute their genera. For this, we consider the fixed fields FH, of F, under subgroups H of G, where G = Aut(F/F9) is the automor phism group of F/Fg. In this thesis, we show how one can compute the genera of FH for various subgroups H of G. Our computation here is based on the facts that: G is a Ree group which acts as a permutation group on the set of rational places of F and this action of G is nothing but the usual 2-transitive representation of the Ree group.


Explicit maximal and minimal curves over finite fields of odd characteristics
Özbudak, Ferruh (2016-11-01)
In this work we present explicit classes of maximal and minimal Artin-Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1].
The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace
Çakıroğlu, Yağmur; Yayla, Oğuz; Yılmaz, Emrah Sercan (2022-08-01)
We present the formula for the number of monic irreducible polynomials of degree n over the finite field F-q where the coefficients of x(n)(-1) and x vanish for n >= 3. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements a is an element of F-qn for which Trace(a) = 0 and Trace(a(-1)) = 0.
Coşkun, Emre; Mustopa, Yusuf (2012-01-01)
Given a general ternary form f = f(x(1), x(2), x(3)) of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces and van den Bergh's correspondence between representations of the generalized Clifford algebra C f associated to f and Ulrich bundles on the surface X f := {w(4) = f(x(1), x(2), x(3))}. P-3 to construct a positive-dimensional family of 8-dimensional irreducible representations of C-f.
Quadratic forms of codimension 2 over certain finite fields of even characteristic
Özbudak, Ferruh; Saygi, Zulfukar (2011-12-01)
Let F-q be a finite field of characteristic 2, not containing F-4. Let k >= 2 be an even integer. We give a full classification of quadratic forms over F-q(k) of codimension 2 provided that certain three coefficients are from F-4. We apply this to the classification of maximal and minimal curves over finite fields.
The geometry of self-dual two-forms
Bilge, AH; Dereli, T; Kocak, S (1997-09-01)
We show that self-dual two-forms in 2n-dimensional spaces determine a n(2)-n+1-dimensional manifold S-2n and the dimension of the maximal linear subspaces of S-2n is equal To the (Radon-Hurwitz) number of linearly independent vector fields on the sphere S2n-1. We provide a direct proof that for n odd S-2n has only one-dimensional linear submanifolds. We exhibit 2(c)-1-dimensional subspaces in dimensions which are multiples of 2(c), for c=1,2,3. In particular, we demonstrate that the seven-dimensional linear...
Citation Formats
E. Çakçak, “Subfields of the function field of the deligne-Lusztig curve of ree type,” Ph.D. - Doctoral Program, Middle East Technical University, 2002.